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Question
If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n)
Solution
Let a be the first term and d be the common difference of the given A.P. Then,
pth term = q ⇒ a + (p – 1) d = q ….(i)
qth term = p ⇒ a + (q – 1) d = p ….(ii)
Subtracting equation (ii) from equation (i),
we get
(p – q) d = (q – p) ⇒ d = – 1
Putting d = – 1 in equation (i), we get
a = (p + q – 1)
nth term = a + (n – 1) d
= (p + q – 1) + (n – 1) × (–1) = (p + q – n)
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